Algebra Examples

$2^{x - 1} > 32$

Step 1

Create equivalent expressions in the equation that all have equal bases.

$2^{x - 1} > 2^{5}$

Step 2

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$x - 1 > 5$

Step 3

Move all terms not containing $x$ to the right side of the inequality.

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Step 3.1

Add $1$ to both sides of the inequality.

$x > 5 + 1$

Step 3.2

Add $5$ and $1$ .

$x > 6$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x > 6$

Interval Notation:

$(6, \infty)$

Step 5